Related papers: Alberti's type rank one theorem for martingales
The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…
We introduce a scale of weighted Carleson norms, which depend on an integrability parameter p, where p=2 corresponds to the classical Carleson measure condition. Relations between the weighed BMO norm of a vector-valued function f:R->X, and…
A vector-valued version of the Girsanov theorem is presented, for a scalar process with respect to a Banach-valued measure. Previously, a short discussion about the Birkhoff-type integration is outlined, as for example integration by…
We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal…
Given a probability space $(\Omega, \mathsf{A}, \mu)$, let $\mathsf{A}_1, \mathsf{A}_2, ...$ be a filtration of $\sigma$-subalgebras of $\mathsf{A}$ and let $\mathsf{E}_1, \mathsf{E}_2, ...$ denote the corresponding family of conditional…
We define a class of discrete abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply…
We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of…
Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…
In the paper, we give the proof of the polar decomposition of the Wiener measure according to the orbits of the group of diffeomorphisms.
We prove that every element of the polar cone to the closed convex cone of monotone transport maps can be represented as the divergence of a measure field taking values in the positive definite matrices.
Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this…
We prove uniqueness of a decomposition of $1$ into indecomposable Hermitian idempotents in an order of a finite-dimensional $\mathbb{Q}$-algebra with positive involution, by generalising a result of Eichler on unique decomposition of…
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker…
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
We note that Pillay's result on the stability of an algebraically closed field with a predicate for a group of Lang type implies that number uniformity follows formally from the finiteness results analogous to Faltings' Theorem.
In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the…
The inverse question of identifying a function from the nodes (zeroes) of its wavelet transform arises in a number of fields. These include whether the nodes of a heat or hypoelliptic equation solution determine its initial conditions, and…
Unfortunately, yes, it is. In ref.[1] it has been shown that without fixing the reaction-amplitude phase, many combinations of partial waves at neighboring energies in single-energy, single-channel partial wave analysis reproduce…
We consider the polar factorization of vector valued mappings introduced by Y. Brenier. In the case of a family of mappings depending on a parameter. We investigate the regularity with respect to this parameter of the terms of the polar…
We classify the reflexive modules of rank one over rational and minimally elliptic singularities. Equivalently, we classify full line bundles on the resolutions of rational and minimally elliptic singularities. As an application, we…